The square and add Markov chain

Abstract

Squaring and adding $\pm 1$ mod p generates a curiously intractable random walk. A similar process over the finite field ${\mathbf{F}}_q$ (with $q=2^d$) leads to novel connections between elementary Galois theory and probability.

16 pages. Comments are welcome!

References in corpus (1)

• Mixing time of the Chung--Diaconis--Graham random process

Cited by in corpus (1)

• Markov chains on finite fields with deterministic jumps